at Google ScholarTitle data
Björnsson, Jóhann ; Giesl, Peter ; Hafstein, Sigurdur Freyr ; Kellett, Christopher M. ; Li, Huijuan:
Computation of continuous and piecewise affine Lyapunov functions by numerical approximations of the Massera construction.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2014
. - 6 p.
Project information
| Project title: |
Project's official title Project's id Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO) 264735-SADCO The Icelandic Research Fund, Grant 130677- 052 ARC Future Fellowship FT1101000746 Humboldt Research Fellowship No information |
|---|
Abstract in another language
The numerical construction of Lyapunov functions provides useful information on system behavior. In the Continuous and Piecewise Affine (CPA) method, linear programming is used to parameterize a CPA Lyapunov function for continuous nonlinear systems. This method is relatively slow due to the linear program that has to be solved. A recent proposal was to parameterize the CPA Lyapunov function based on a Lyapunov function in a converse Lyapunov theorem by Yoshizawa. In this paper we propose parameterizing CPA Lyapunov functions using a Lyapunov function construction in a classic converse Lyapunov theorem by Massera. We provide the theory for such a parameterization and present several examples to illustrate the utility of this approach.
Further data
| Item Type: | Preprint, postprint |
|---|---|
| Keywords: | Lyapunov methods; nonlinear control systems; asymptotic stability; linear programming; Massera construction; approximation methods; continuous systems |
| Institutions of the University: | Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Profile Fields Profile Fields > Advanced Fields Profile Fields > Advanced Fields > Nonlinear Dynamics |
| Result of work at the UBT: | Yes |
| DDC Subjects: | 500 Science > 510 Mathematics |
| Date Deposited: | 28 Mar 2015 22:00 |
| Last Modified: | 30 Mar 2015 07:13 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/9470 |
Available Versions of this Item
- Computation of continuous and piecewise affine Lyapunov functions by numerical approximations of the Massera construction. (deposited 28 Mar 2015 22:00) [Currently Displayed]